Stacks and the homotopy theory of simplicial sheaves

John F. Jardine

Type: Article

Publication Date: 2001-01-01

Citations: 30

DOI: https://doi.org/10.4310/hha.2001.v3.n2.a5

Abstract

Stacks are described as sheaves of groupoids G satisfying an effective descent condition, or equivalently such that the classifying object BG satisfies descent.The set of simplicial sheaf homotopy classes [ * , BG] is identified with equivalence classes of acyclic homotopy colimits fibred over BG, generalizing the classical relation between torsors and non-abelian cohomology.Group actions give rise to quotient stacks, which appear as parameter spaces for the separable transfer construction in special cases.

Locations

Project Euclid (Cornell University) - View - PDF
Homology Homotopy and Applications - View - PDF

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